Question

The vertices of polygon ABCD are given as A(1, 1), B(2, 3), C(3, 2), and D(0, 1). ABCD is reflected across the x-axis and translated. Match each vertex of polygon ABCD to its coordinates.

a) A: (1, -1); B: (2, -3); C: (3, -2); D: (0, -1)
b) A: (1, -1); B: (2, -3); C: (3, -2); D: (0, -1)
c) A: (1, -1); B: (2, -3); C: (3, -2); D: (0, -1)
d) A: (1, -1); B: (2, -3); C: (3, -2); D: (0, -1)

Answer 1

After reflecting the vertices of polygon ABCD across the x-axis, the coordinates are A(1, -1), B(2, -3), C(3, -2), and D(0, -1). The options provided (a, b, c, d) are all identical, reflecting the shape across the x-axis with no additional translation applied.

Step-by-step explanation:

Reflecting a point across the x-axis will change the sign of its y-coordinate but leave the x-coordinate unchanged. After the reflection across the x-axis, the coordinates of A, B, C, and D will become A(1, -1), B(2, -3), C(3, -2), and D(0, -1) respectively. Without specific translation values, we can only determine the result of the reflection. Thus, each reflected vertex matches with A: (1, -1), B: (2, -3), C: (3, -2), and D: (0, -1). All four options (a), (b), (c), and (d) provided in the question are identical and correctly match the result of reflecting polygon ABCD across the x-axis. If no further translation is applied, then the matching coordinates would indeed be those listed.